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Riemann-Roch for tensor powers

Riemann-Roch for tensor powers Mapping a locally free module on a scheme to its l-th tensor power gives rise to a natural map from the Grothendieck group of all locally free modules to the Grothendieck group of all locally free representations of the l-th symmetric group. In this paper, we prove some formulas of Riemann-Roch type for the behavior of this tensor power operation with respect to the push-forward homomorphism associated with a projective morphism between schemes. We furthermore establish analogous formulas for higher K-groups. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Riemann-Roch for tensor powers

Mathematische Zeitschrift , Volume 233 (4) – Apr 1, 2000

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References (34)

Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Berlin Heidelberg
Subject
Legacy
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s002090050497
Publisher site
See Article on Publisher Site

Abstract

Mapping a locally free module on a scheme to its l-th tensor power gives rise to a natural map from the Grothendieck group of all locally free modules to the Grothendieck group of all locally free representations of the l-th symmetric group. In this paper, we prove some formulas of Riemann-Roch type for the behavior of this tensor power operation with respect to the push-forward homomorphism associated with a projective morphism between schemes. We furthermore establish analogous formulas for higher K-groups.

Journal

Mathematische ZeitschriftSpringer Journals

Published: Apr 1, 2000

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